Two transistors are needed for an integrated circuit. Of the eight available, three have broken insulation layers, two have poor diodes, and three are in good condition. Two transistors are selected at random.

(a) Find the joint probability distribution of \(X_{1}=\) the number of transistors with broken insulation layers and \(X_{2}=\) the number having poor diodes.

(b) Find the probability of 1 or 2 total defects among the two selected.

(c) Find the marginal probability distribution of \(X_{2}\).

(d) Find the conditional probability distribution of \(X_{2}\) given \(X_{1}=0\).